We propose a new numerical approach for the solution of the 2D acoustic wave equation to model the predicted data in the field of active-source seismic inverse problems. This method consists in using an explicit finite difference technique with an adaptive order of approximation of the spatial derivatives that takes into account the local velocity at the grid nodes. Testing our method to simulate the recorded seismograms in a marine seismic acquisition, we found that the low computational time and the low approximation error of the proposed approach make it suitable in the context of seismic inversion problems.
If the inline PDF is not rendering correctly, you can download the PDF file here.
1. A. Tarantola A strategy for nonlinear elastic inversion of seismic reection data Geophysics vol. 51 no. 10 pp. 1893-1903 1986.
2. J. Virieux and S. Operto An overview of full-waveform inversion in exploration geophysics Geophysics vol. 74 no. 6 pp. WCC1-WCC26 2009.
3. R. Alford K. Kelly and D. M. Boore Accuracy of finite-difference modeling of the acoustic wave equation Geophysics vol. 39 no. 6 pp. 834- 842 1974.
4. J. Virieux V. Cruz-Atienza R. Brossier E. Chaljub O. Coutant S. Garambois D. Mercerat V. Prieux S. Operto A. Ribodetti et al. Modelling seismic wave propagation for geophysical imaging. Intech 2016.
5. R. E. Sheriff and L. P. Geldart Exploration seismology. Cambridge university press 1995.
6. Ö. Yilmaz Seismic data analysis: Processing inversion and interpre- tation of seismic data. Society of exploration geophysicists 2001.
7. A. Fichtner Full seismic waveform modelling and inversion: Springer science & business media 2011.
8. A. Sajeva M. Aleardi E. Stucchi N. Bienati and A. Mazzotti Estimation of acoustic macro models using a genetic full-waveform inversion: Applications to the marmousi model Geophysics 2016.
9. A. Tognarelli E. Stucchi N. Bienati A. Sajeva M. Aleardi and A. Mazzotti Two-grid stochastic full waveform inversion of 2d marine seismic data in 77th EAGE Conference and Exhibition 2015 2015.
10. C. L. Liner Theory of a 2.5-d acoustic wave equation for constant density media Geophysics vol. 56 no. 12 pp. 2114-2117 1991.
11. Z.-M. Song P. R. Williamson and R. G. Pratt Frequency-domain acoustic-wave modeling and inversion of crosshole data: Part iiinversion method synthetic experiments and real-data results Geo- physics vol. 60 no. 3 pp. 796-809 1995.
12. P. R. Williamson and R. G. Pratt A critical review of acoustic wave modeling procedures in 2.5 dimensions Geophysics vol. 60 no. 2 pp. 591-595 1995.
13. A. R. Mitchell and D. F. Griffths The finite difference method in partial differential equations. John Wiley 1980. 14. K. W. Morton and D. F. Mayers Numerical solution of partial differ- ential equations: an introduction. Cambridge university press 2005.
15. R. Richtmyer and K. Morton Difference methods for initial-value problems. 1967 Interscience New York.
16. J. C. Strikwerda Finite difference schemes and partial differential equa- tions. SIAM 2004.
17. G. C. Cohen Higher-order numerical methods for transient wave equations 2003.
18. B. Fornberg Generation of finite difference formulas on arbitrarily spaced grids Mathematics of computation vol. 51 no. 184 pp. 699- 706 1988.
19. C. Cerjan D. Kosloff R. Kosloff and M. Reshef A nonreecting boundary condition for discrete acoustic and elastic wave equations Geo- physics vol. 50 no. 4 pp. 705-708 1985.
20. R. Courant K. Friedrichs and H. Lewy On the partial difference equations of mathematical physics IBM journal of Research and Develop- ment vol. 11 no. 2 pp. 215-234 1967.
21. C. E. Shannon Communication in the presence of noise Proceedings of the IRE vol. 37 no. 1 pp. 10-21 1949.
22. C. Bunks F. M. Saleck S. Zaleski and G. Chavent Multiscale seismic waveform inversion Geophysics vol. 60 no. 5 pp. 1457-1473 1995.
23. A. Brougois M. Bourget P. Lailly M. Poulet P. Ricarte and R. Versteeg Marmousi model and data in EAEG Workshop-Practical Aspects of Seismic Data Inversion 1990.